Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C53 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11758754 |
| commutator, Fitting, cosocle | C4×C53 | C22 |
| Frattini, hypercenter | C4 | D5×C5⋊D5 |
| socle, prime radical | C2×C53 | D4 |
| hypocenter | C53 | Q16 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,c^2=d,b^a=bc,g^a=g^4,c^b=cd,e^b=e^4,f^b=f^4209 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 553);